{
  "abstract": "Let $\\mathcal{S}^ r$ denote the Schatten--von Neumann class and let $S_{Ψ_{f,λ}}$ be the Schur--Hadamard multiplier whose symbol is the divided-difference matrix of $f$ along $λ$. Let $0<α,r<\\infty$, let $f\\in C^1([-1,1])$ satisfy $f(0)=0$, $|f'(t)|\\lesssim |t|^α$, and let $λ\\in\\ell^r$ be real with $\\|λ\\|_{\\ell^\\infty}\\leq1$. We determine the pairs $0<p,q\\leq\\infty$ for which $S_{Ψ_{f,λ}}:\\mathcal{S}^ q\\to\\mathcal{S}^ p$ is bounded for every such $f$ and $λ$. Our principal new positive estimates treat $q=\\infty,1$ and $0<p<1$. Precisely, we show that the boundedness holds exactly when \\[ \\frac1p\\leq\\fracα{r} +\\min\\!\\left\\{1,\\frac1q\\right\\}. \\] In particular, this resolves the untreated cases in [Arazy, PAMS, 1982] and [Potapov, Sukochev, Tomskova, Adv. Math., 2015]. Our method also delivers a new proof of the main results in just cited papers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17144",
  "author_total": 2,
  "authors": [
    {
      "name": "Jinghao Huang"
    },
    {
      "name": "Fedor Sukochev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49m1q3dnp8k9h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17144",
  "fulltext_url": null,
  "id": "49m1q3dnp8k9h",
  "issns": [],
  "landing_url": "https://hal.science/hal-05740214v1",
  "language": "en",
  "licence": "LicenseRef-publisher-terms",
  "licence_label": "Publisher terms",
  "licence_source": "article",
  "licence_url": "https://hal.science/licences/copyright/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-fa"
    ],
    [
      "hal",
      "1.math.math-oa"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7213381731",
  "pdf_url": "https://hal.science/hal-05740214/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49m1q3dnp8k9h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:29Z",
      "native_id": "hal-05740214",
      "source": "hal",
      "url": "https://hal.science/hal-05740214v1"
    },
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17144",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17144"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "ARAZY'S CONJECTURE CONCERNING SCHUR MULTIPLIERS: REVISITED AND RESOLVED",
  "title_text": "ARAZY'S CONJECTURE CONCERNING SCHUR MULTIPLIERS: REVISITED AND RESOLVED",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/49m1q3dnp8k9h",
  "venue": "HAL",
  "versions": []
}